406 Prof. R. Clausius on the Behaviour of Carbonic Acid 



But now comes the question, In what position do this theo- 

 retical pressure-curve and the horizontal straight line corre- 

 sponding to the actual process stand to each other ? 



James Thomson has expressed no opinion upon it, but has 

 only, in Andrews's figure (reproduced in fig. 1), added to the 

 pressurve-curves referring to the temperatures 13°*1 and 21°*5 

 the curve-portions there drawn in dotted lines. These were 

 probably only intended to give a rough idea of the possible 

 form and position of the portions of the curves. In that form 

 they cannot be accepted as really correct. 



Maxwell, in the first edition of his ( Theory of Heat,' p. 125, 

 goes into the matter more closely. If one of the theoretical 

 continuous pressure-curves, e. g. that belonging to the tem- 

 perature 13°*1, be imagined to be given, and if the horizontal 

 straight line be drawn at different heights, two points a and e 

 are always obtained as the extreme points of the straight line. 

 The difference between the two values possessed by the energy 

 of the substance in the states corresponding to those two 

 points differs in magnitude for the different positions of the 

 straight line. Now, says Maxwell, that position of the straight 

 line at which this difference is a maximum is the correct one. 

 In the fourth edition, however, the passage is altered and the 

 position of the straight line left undetermined. It must there- 

 fore be assumed that Maxwell afterwards relinquished his pre- 

 vious view on this point. 



Van der Waals says (in p. 121 loc. cit.), "I have not suc- 

 ceeded in finding in any of the properties of saturated vapour 

 a characteristic by which it could be determined where the 

 [straight] line must be drawn through the isotherms." 



After this the question what position the horizontal straight 

 line giving the pressure of saturated vapour has in the iso- 

 thermal pressure-curve may well be regarded as still an open 

 one; and I wish to be permitted to communicate here the 

 answer to this question which has presented itself to me on 

 consideration of the subject. 



When the pressure-curve drawn by Andrews and com- 

 pleted by James Thomson for the temperature of 13°*1, is ex- 

 amined, it is seen to be single from m to a and again from e 

 to n, while it is double between a and e. Between the two 

 states of the substance corresponding to the points a and e (and 

 which we will briefly name states a and e) there are conse- 

 quently two ways in which the substance can pass out of the 

 one into the other. The transition can take place on both of 

 these paths, under perfectly similar circumstances, in the direc- 

 tion from a to e and also in the direction from eio a\ the 

 respective changes are therefore both to be designated as re- 

 versible. 



